Area of Composite Figures

Active learning helps students visualize how composite figures are made of simpler shapes, which builds confidence in breaking down complex problems. Hands-on work with cutouts and measurements makes abstract area concepts concrete and easier to remember.

• Primary 4
• Mathematics
• 4 activities
• 20 min–45 min

Learning Objectives

1. Calculate the area of composite figures by decomposing them into rectangles.
2. Analyze diagrams to identify necessary measurements for calculating the area of individual rectangles within a composite figure.
3. Demonstrate the process of finding the area of a composite figure by subtracting the area of a smaller rectangle from a larger one.
4. Explain the strategy used to find the total area of a composite figure, whether by addition or subtraction of component areas.

Stations Rotation

⏱ 45 min·Small Groups

Stations Rotation: Shape Breakdown Stations

Prepare four stations with composite figures on grid paper: one for addition, one for subtraction, one for irregular outlines, one for real-world maps. Students decompose, calculate areas, and record steps at each. Rotate groups every 10 minutes, then share findings.

Prepare & details

How do you break a composite figure into simpler rectangles to find its total area?

Facilitation Tip: During Shape Breakdown Stations, provide scissors and grid paper to allow students to physically separate shapes and label dimensions clearly.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Problem-Based Learning

⏱ 30 min·Pairs

Pairs Challenge: Build and Measure

Pairs draw a composite figure using rulers on grid paper, label dimensions, then swap with another pair to decompose and calculate area. They verify by cutting shapes apart and measuring separately. Discuss differences in methods.

Prepare & details

What information from a diagram do you need in order to calculate the area of each part?

Facilitation Tip: For Build and Measure, circulate with a checklist to ensure pairs verify each other’s measurements before recording calculations.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Problem-Based Learning

⏱ 35 min·Whole Class

Whole Class: Area Puzzle Relay

Divide class into teams. Project a large composite figure; first student decomposes one part on board, next calculates its area, and so on until complete. Teams race while explaining steps aloud.

Prepare & details

Can you find the area of a shape by subtracting one rectangle from another, and show your working?

Facilitation Tip: In the Area Puzzle Relay, place answer keys at stations so teams can self-check their progress before moving on.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Problem-Based Learning

⏱ 20 min·Individual

Individual: Cut-Out Composites

Provide worksheets with composite shapes to cut along lines into rectangles. Students measure, compute areas, reassemble, and explain their breakdown in writing.

Prepare & details

How do you break a composite figure into simpler rectangles to find its total area?

Facilitation Tip: During Cut-Out Composites, ask students to trace each rectangle in a different colored pencil to visually track non-overlapping parts.

Setup: Groups at tables with access to research materials

Materials: Problem scenario document, KWL chart or inquiry framework, Resource library, Solution presentation template

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management
• Relationship Skills

Teaching This Topic

Teach students to always sketch the figure and label every dimension they see before starting calculations. Avoid rushing to formulas; emphasize drawing lines to divide the shape and writing the area formula for each part. Research shows this step-by-step approach reduces errors and builds lasting understanding.

What to Expect

Students will confidently decompose composite figures into rectangles, calculate each area carefully, and combine results with clear working. They will explain their steps and check for overlapping areas or missing parts in diagrams.

Watch Out for These Misconceptions

Common Misconception

During Shape Breakdown Stations, watch for students who add areas of all visible rectangles without subtracting overlapping parts.

What to Teach Instead

Have students physically separate overlapping cutouts and place them side by side to see the double-counted space, then guide them to subtract the overlapping area from the total.

Common Misconception

During Build and Measure, watch for students misreading diagram dimensions, like confusing length for height.

What to Teach Instead

Ask students to highlight labels with colored pencils during the build and pair-share their measurements before recording calculations to catch mismatches early.

Common Misconception

During Area Puzzle Relay, watch for students calculating perimeter instead of area for the whole shape.

What to Teach Instead

Contrast tasks on grid paper by having students trace boundaries for perimeter and fill interiors for area, then discuss the difference during the relay reflection.

Common Misconception

Assessment Ideas

Exit Ticket

Provide students with a diagram of a composite figure made of two rectangles. Ask them to: 1. Label the dimensions of each smaller rectangle. 2. Write the formula for the area of each. 3. Calculate the total area and show their working.

Quick Check

Display a composite figure where one rectangle is 'cut out' from a larger rectangle. Ask students to write down the calculation needed to find the shaded area, for example, 'Area of Big Rectangle - Area of Small Rectangle'.

Discussion Prompt

Present two different composite figures. Ask students: 'How are these figures similar in how we find their area? How are they different? Which strategy do you prefer and why?'

Extensions & Scaffolding

• Challenge: Provide a composite figure with missing side lengths. Students must derive unknown sides using given areas before calculating the total.
• Scaffolding: Give students pre-cut rectangles with labeled sides to assemble before calculating areas individually.
• Deeper exploration: Introduce figures with three or more shapes and ask students to compare two different decomposition strategies in a written reflection.

Key Vocabulary

Composite Figure	A shape made up of two or more simple geometric shapes, such as rectangles.
Decomposition	The process of breaking down a complex shape into smaller, simpler shapes.
Area	The amount of two-dimensional space a shape occupies, measured in square units.
Length	The longer side of a rectangle.
Breadth	The shorter side of a rectangle, also known as width.